Lab #1 Measurement Purpose
The purpose of this lab was to investigate the process of measurement and the accuracy of different measuring instruments.
Hypothesis
It is hypothesized that the measurements taken in this lab will be very close to the actual values. The equipment used for measuring is accurate and should be precise. It is estimated that the percent error will be around 5% to 10%. Without human error or rounding, the percent error could be 0%, but this is not possible.
Apparatus
Ruler
Card
Micrometer
Vernier caliper
2 blocks
2 spheres
2 cylinders
Balance
Procedure
Part A: Take a note card and measure the length and width of the card, in centimeters. Then, measure the length and width again, but in inches. Find the mean, standard deviation, and percent deviation. Calculate the area of the card as well as the error and percent error. The accepted value is 2.540 cm/in.
Part B: Choose a block to measure, measure the length, width and height in both centimeters and inches. Repeat this three times, recording the data on the chart. Calculate the average length, width, and height of the block for both systems, use the average values to calculate the volume of the block. Find the experimental conversion factor by dividing the average volume in cubic centimeters by the volume in cubic inches. The accepted value is 16.39 cm³/in³. Last, find the error and percent error. Take a different block repeat these steps.
Part C: Choose a metal cylinder, measure the length and diameter of the cylinder using a Vernier caliper. Take three trials and record the data. Using the average radius and length, calculate the volume of the cylinder. Record the mass of the cylinder, in grams, on a balance. Find the mass density of the cylinder and compare it to the accepted value which was 1.36 g/cm³ for both cylinders used. Repeat these steps with a different cylinder.
Part D: Choose a sphere, measure the diameter using a micrometer. Mass the sphere and record the data. Calculate the mass density and compare it to the accepted mass density which was 7.8 and 1.15 g/cm³. Repeat the steps above with a different sphere. Data:
Part A:
Trial
Length L
Width W
Length L
Width W
No.
Cm
Cm
In
In
1
20.21
7.18
8.00
2.81
2
20.19
7.12
7.94
2.81
3
20.16
7.17
8.00
2.81
4
20.17
7.16
7.94
2.81
5
20.18
7.17
8.00
2.81
6
20.30
7.12
7.94
2.81
7
20.31
7.11
8.00
2.81
8
20.31
7.12
7.94
2.81
9
20.30
7.12
8.00
2.81
10
20.29
7.13
7.94
2.81
Length:
Mean: 20.24 cm
Average Deviation: .07 cm
% Deviation: 7%
Mean: 7.97 in
Average deviation .031 in
% Deviation: 3.1% Width:
Mean: 7.14 cm
Average Deviation: .024 cm
% Deviation: 2.4%
Mean: 2.81
Average Deviation: 0 in
% Deviation: 0% Area:
Volume of sphere- V=3/4πr³ Experimental mass density = 65.76g/13.33cm³=4.93g/cm³ Error=4.93-7.8=2.87g/cm³ error= (4.93-7.8)/7.8 x100=36.79%Experimental mass density = 9.85g/12.719cm³=.774g/cm³Error=1.15-.774=.376g/cm³ error= (.376-1.15)/1.15 x100=32.66%
The unit analysis shows that most of the measurements were fairly accurate. A few measurements may have been off because of the tool being used and human error. The largest error was 49.12% which is very high but most of the others were much closer. Conclusion:
The hypothesis which stated that the percent error of measurements would be 5% to 10% was proved false. The majority of measurements were off by larger numbers such as the measurements of the spheres. Sphere one had a 36.79% error while sphere two had a 32.66% error. Both these percent errors are far above the 5% to 10% range. The tools being used were fairly accurate, but some rounding was necessary at some points. In the future, measuring tools could be made even more precise as well as easier to read to reduce human error. Also, some of the materials can get confusing as to which accepted mass density goes with which. All in all, the lab was a good way to practicing measuring with various tools as well as, learning the density formulas and computing.
Purpose
The purpose of this lab was to investigate the process of measurement and the accuracy of different measuring instruments.
Hypothesis
It is hypothesized that the measurements taken in this lab will be very close to the actual values. The equipment used for measuring is accurate and should be precise. It is estimated that the percent error will be around 5% to 10%. Without human error or rounding, the percent error could be 0%, but this is not possible.
Apparatus
- Ruler
- Card
- Micrometer
- Vernier caliper
- 2 blocks
- 2 spheres
- 2 cylinders
- Balance
ProcedurePart A: Take a note card and measure the length and width of the card, in centimeters. Then, measure the length and width again, but in inches. Find the mean, standard deviation, and percent deviation. Calculate the area of the card as well as the error and percent error. The accepted value is 2.540 cm/in.
Part B: Choose a block to measure, measure the length, width and height in both centimeters and inches. Repeat this three times, recording the data on the chart. Calculate the average length, width, and height of the block for both systems, use the average values to calculate the volume of the block. Find the experimental conversion factor by dividing the average volume in cubic centimeters by the volume in cubic inches. The accepted value is 16.39 cm³/in³. Last, find the error and percent error. Take a different block repeat these steps.
Part C: Choose a metal cylinder, measure the length and diameter of the cylinder using a Vernier caliper. Take three trials and record the data. Using the average radius and length, calculate the volume of the cylinder. Record the mass of the cylinder, in grams, on a balance. Find the mass density of the cylinder and compare it to the accepted value which was 1.36 g/cm³ for both cylinders used. Repeat these steps with a different cylinder.
Part D: Choose a sphere, measure the diameter using a micrometer. Mass the sphere and record the data. Calculate the mass density and compare it to the accepted mass density which was 7.8 and 1.15 g/cm³. Repeat the steps above with a different sphere.
Data:
Part A:
Mean: 20.24 cm
Average Deviation: .07 cm
% Deviation: 7%
Mean: 7.97 in
Average deviation .031 in
% Deviation: 3.1%
Width:
Mean: 7.14 cm
Average Deviation: .024 cm
% Deviation: 2.4%
Mean: 2.81
Average Deviation: 0 in
% Deviation: 0%
Area:
Area: 144.51 cm²
Area: 22.42 in²
Experimental conversion factor: 2.539 cm/in
Accepted Value: 2.540 cm³/in³
Error: .01 cm/in
% Error: .3937%
Part B: Block 1
Average volume: 5.25 in³
Experimental conversion factor: 15.71 cm³/in³
Accepted Value: 2.540 cm³/in³
Error: .6797
% Error: 4.15%
Block 2
Average volume: 4.369 in³
Experimental conversion factor: 15.13 cm³/in³
Accepted Value: 16.39 cm³/in³
Error: 1.26 cm³/in³
% Error: 7.69%
Part C:
Cylinder 1
Mass: 22.28g
Experimental mass density 1.639 g/cm³
Accepted mass density: 1.36 g/cm³
Error: .279 g/cm³
% Error: 20.51%
Cylinder 2
Mass: 25.61 g
Experimental mass density: 2.02 g/cm³
Accepted mass density: 1.36 g/cm³
Error: .668 g/cm³
% Error: 49.12%
Part D: Sphere 1
Mass: 65.76 g
Experimental mass density: 4.93 g/cm³
Accepted mass density: 7.8 g/cm³
Error: 2.87 g/cm³
% Error: 36.79%
Sphere 2
Mass: 9.85 g
Experimental mass density: .774 g/cm³
Accepted mass density: 1.15 g/cm³
Error: .376 g/cm³
% Error: 32.66%
Analysis:
Mean Value= (20.21+20.19+20.16+20.17+20.18+20.3+20.31+20.31+20.3+20.29)/10
Average Deviation= |average-each value|
Percent Deviation= average deviation x100Error= 2.53-2.54=.01%
Error= (2.53-2.54)/2.54 x100=.394%
Volume= length x width x height
Experimental conversion factor=82.46cm3/5.25in3=15.71 cm3/in3Error= 15.71cm³/in³-16.39cm³/in³=0.683cm³/in³ error= (15.71-16.39)/16.39 x100=4.15%
Volume of cylinder- V=πr²L
Experimental conversion factor= 22.28g/13.59cm³=1.639g/cm³
Error=.1.639-1.36=.279g/cm³ error= (.279-1.36)/1.36 x100=20.51%
Experimental conversion factor= 25.61g/12.63cm³=2.02g/cm³Error= 2.02-1.36=.668g/cm³ error= (2.02-1.36)/1.36 x100=49.12%
Volume of sphere- V=3/4πr³
Experimental mass density = 65.76g/13.33cm³=4.93g/cm³
Error=4.93-7.8=2.87g/cm³ error= (4.93-7.8)/7.8 x100=36.79%Experimental mass density = 9.85g/12.719cm³=.774g/cm³Error=1.15-.774=.376g/cm³ error= (.376-1.15)/1.15 x100=32.66%
The unit analysis shows that most of the measurements were fairly accurate. A few measurements may have been off because of the tool being used and human error. The largest error was 49.12% which is very high but most of the others were much closer.
Conclusion:
The hypothesis which stated that the percent error of measurements would be 5% to 10% was proved false. The majority of measurements were off by larger numbers such as the measurements of the spheres. Sphere one had a 36.79% error while sphere two had a 32.66% error. Both these percent errors are far above the 5% to 10% range. The tools being used were fairly accurate, but some rounding was necessary at some points. In the future, measuring tools could be made even more precise as well as easier to read to reduce human error. Also, some of the materials can get confusing as to which accepted mass density goes with which. All in all, the lab was a good way to practicing measuring with various tools as well as, learning the density formulas and computing.